ill health vs unhealthiness

ill health and unhealthiness both are nouns.

Word	Noun	Adjective	Verb	Adverb
ill health	Yes	No	No	No
unhealthiness	Yes	No	No	No

As nouns, ill health and unhealthiness are synonyms defined as:

ill health and unhealthiness: a state in which you are unable to function normally and without pain

Other synonyms of ill health include health problem.

ill health (noun)	unhealthiness (noun)
a state in which you are unable to function normally and without pain	a state in which you are unable to function normally and without pain